You get than in most fiction. Any time a master takes an apprentice. But after they've become the apprentice the story needs to move on, so they don't keep harping on the point. Consider Yoda / Luke Skywalker.
This sort of ritualized "reluctance" is central to storytelling. For example in the standard hero's journey structure there's a point called the "refusal of the call". This is where the hero, in his ordinary life rejects the call to go off on the adventure, but then fate or somesuch kicks his backside to actually go do Hero Things.
But usually they forget about the issues raised after that point, because it's merely a structural thing to show obstacles rather than a plot point. I'd say a mentor being reluctant to help the hero is merely there to show an obstacle that the hero must overcome, so things aren't shown to happen too easily.
Again, it's not actually a plot point or theme the narrative is trying to address, it's a structural thing needed to make certain types of scenes flow better. Imagine the opposite: the hero asks the master to teach him, master instantly says "ok no problem" and then it's into the training montage. This would just feel more artificial than if there's some resistance from the master to providing the training. If the hero has to prove his worth and people don't keep falling over backwards to help him, it makes it feel less like a Gary Stu world.
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Topic: I like anime, do you like anime? (Read 3142431 times)